Equivalent Parallel Mechanisms Research Articles

Design and optimization of a novel sagittal-plane knee exoskeleton with remote-center-of-motion mechanism

Powered exoskeleton is a wearable robot that can provide power-assisted motion for the human body. One of the challenges in the exoskeleton research is how to improve its kinematic synergy. In this paper, a novel knee exoskeleton robot is designed to improve the kinematic synergy between the exoskeleton and the human body. The novel exoskeleton adopts the sagittal-plane layout to reduce the bias moment, and uses a remote-center-of-rotation mechanism to ensure the coincidence of the rotation centers of the exoskeleton and the human body. To analyze the influence of the interaction error on the performance of the exoskeleton, this paper proposes a human-exoskeleton fusion model based on the virtual equivalent parallel mechanism method, and parameterize the interaction error through virtual kinematic chains. Finally, the assisting performance of the novel exoskeleton is analyzed and verified through simulation experiments, motion experiments, body motion experiments and human simulation experiments. The human-exoskeleton fusion model proposed in this paper has positive significance for the configuration design, biomechanical analysis and application of exoskeleton robots.

Inverted Modelling: An Effective Way to Support Motion Planning of Legged Mobile Robots

This paper presents an effective way to support motion planning of legged mobile robots—Inverted Modelling, based on the equivalent metamorphic mechanism concept. The difference from the previous research is that we herein invert the equivalent parallel mechanism. Assuming the leg mechanisms are hybrid links, the body of robot being considered as fixed platform, and ground as moving platform. The motion performance is transformed and measured in the body frame. Terrain and joint limits are used as input parameters to the model, resulting in the representation which is independent of terrains and particular poses in Inverted Modelling. Hence, it can universally be applied to any kind of legged robots as global motion performance framework. Several performance measurements using Inverted Modelling are presented and used in motion performance evaluation. According to the requirements of actual work like motion continuity and stability, motion planning of legged robot can be achieved using different measurements on different terrains. Two cases studies present the simulations of quadruped and hexapod robots walking on rugged roads. The results verify the correctness and effectiveness of the proposed method.

Optimum Design for a New Reconfigurable Two-Wheeled Self-Balancing Robot Based on Virtual Equivalent Parallel Mechanism

Abstract Two-wheeled self-balancing robot (TWSBR) is a mobile robot with a wide application in security, rescue, entertainment, and other fields. To make the robot obtain a larger range of the controllable inclination angle, a reconfigurable mechanism of the moment of inertia is designed for the TWSBR, and the energy consumption of the reconfigurable mechanism is reduced by a gravity compensation mechanism. This paper constructs a virtual equivalent parallel mechanism (VEPM) to model the robot-ground system combining the robot and the ground. The kinematics, dynamic model, and performance indexes of the VEPM are solved based on the vector method, the Lagrangian dynamics, and the screw theory. Then, the dimensions of the mechanism are optimized based on the comprehensive performance analysis. Finally, the effectiveness of the optimization algorithm and gravity compensation mechanism is verified through simulation and motion experiments. The reconfigurable mechanism enables the TWSBR to stand up, step up, and surmount obstacles. The performance analysis and optimal design approaches proposed in this paper have positive significance for the systematic modeling and optimal design of two-wheeled and two-legged robots.

A new comprehensive performance optimization approach for Earth-contact mechanism based on terrain-adaptability task

AbstractEarth-contact mechanism (ECM), a type of mechanism to keep the system in contact with the earth and to move with the terrain changes. This paper uses the virtual equivalent parallel mechanism (VEPM) to convert the terrain data into the kinematical variables of the moving platform in the VEPM, and further analyzes the performance of the VEPM at each terrain point. Then, the comprehensive performance of the VEPM is chosen as the optimization goal, and a task-oriented dimensional optimization approach combined with the particle swarm algorithm and the neural network algorithm is proposed. This paper conducted a comparative experiment to verify the superiority of the new approach in optimizing the ECM’s comprehensive performance, whose performance analysis also can be applied into the layout design of the ECM. This paper proposed an analysis method to construct the ECM’s performance map based on the digital terrain map, which helps the control system and operator to make the optimal control decision.

Conceptual design and analysis of legged landers with orientation capability

The lander with orientation capability is of fundamental importance for the “Returning” mission because its body can be the base with a suitable launching angle for the ascender lifting off. This paper proposes the conceptual design and verification of Landers with Orientation Capability (LOCs). Firstly, the topological composition of the lander is analyzed and expressed in the form of Lie group, which provides the fundamental principle for the type synthesis of LOCs. Then, the type synthesis approach for designing LOCs is proposed, which includes designing the Equivalent Parallel Mechanism (EPM) and the auxiliary limbs. Numerous mechanisms of LOCs with two-dimensional rotational motions are obtained based on the type synthesis approach by developing and combining the EPMs and auxiliary limbs. Afterward, kinematics and Jacobian matrix of a typical legged lander are developed, the workspace is analyzed, singularity configurations are analyzed based on the wrench graph method, and finally, the orientation capability is analyzed. The pitch and yaw angle reach 17.5°, considering the permissible range of joints. The proposed types of LOCs offer potential candidate for the “Returning” mission of the exploration mission.

A method for comprehensive performance optimization of four-leg landing gear based on the virtual equivalent parallel mechanism

Taking-off and landing on unstructured terrain can effectively expand the application of aircrafts. The terrain-adaptive taking-off and landing technology is achieved through adaptive landing gear. The performance of the adaptive landing gear determines the safety performance of the aircraft during taking-off and landing. This paper proposes a comprehensive performance optimization method for four-leg landing gears based on the virtual equivalent parallel mechanism (VEPM). This method associates the motion variables of the parallel mechanism with the terrain data, and combines the original mechanism to form a VEPM. By analyzing the comprehensive performance of the equivalent parallel mechanism, the particle swarm algorithm is used to optimize the dimensions of the landing gear mechanism. The new optimization method can enhance the comprehensive performance of the landing gear mechanism, which contributes to the structural design and optimal control of the terrain-adaptive landing gear.

Different manipulation mode analysis of a radial symmetrical hexapod robot with leg\u2014arm integration

With the widespread application of legged robot in various fields, the demand for a robot with high locomotion and manipulation ability is increasing. Adding an extra arm is a useful but general method for a legged robot to obtain manipulation ability. Hence, this paper proposes a novel hexapod robot with two integrated leg—arm limbs that obtain dexterous manipulation functions besides locomotion ability without adding an extra arm. The manipulation modes can be divided into coordinated manipulation condition and single-limb manipulation condition. The former condition mainly includes fixed coordinated clamping case and fixed coordinated shearing case. For the fixed coordinated clamping case, the degrees of freedom (DOFs) analysis of equivalent parallel mechanism by using screw theory and the constraint equation of two integrated limbs are established. For the fixed coordinated shearing case, the coordinated working space is determined, and an ideal coordinated manipulation ball is presented to guide the coordinated shearing task. In addition, the constraint analysis of two adjacent integrated limbs is performed. Then, mobile manipulation with one integrated leg—arm limb while using pentapod gait is discussed as the single-limb manipulation condition, including gait switching analysis between hexapod gait and pentapod gait, different pentapod gaits analysis, and a complex six-DOF manipulation while walking. Corresponding experiments are implemented, including clamping tasks with two integrated limbs, coordinated shearing task by using two integrated limbs, and mobile manipulation with pentapod gait. This robot provides a new approach to building a multifunctional locomotion platform.

Constraint characteristics and type synthesis of two families of 1T2R parallel mechanism

AbstractPU- and P*U*-equivalent parallel mechanisms (PMs) are critical families of PMs with one translational and two rotational (1T2R) degree of freedoms and have always been a research hotspot among lower mobility PMs. However, researches on these two families of PMs remain to be inadequate, and existing types are few and uncomprehensive. In this study, first, general wrench systems of PU-equivalent are derived based on virtual-chain approach and screw theory, revealing its constraint characteristics under general configuration. Cause of one parasitic motion is put forward and general wrench systems of P*U*-equivalent PMs with one parasitic motion are obtained. In addition, constraint analysis has been carried out to figure out constraint characteristics of P*U*-equivalent PMs with three parasitic motions. Second, branch chains are divided by generating constraints, and their structures are synthesized based on the presented rules. Then, the process for type synthesis of PU-equivalent PMs and P*U*-equivalent PMs and a series of novel 1T2R PMs are attained based on this. Finally, a novel PU-equivalent PM, 2PRU-PRUPc, and a novel P*U*-equivalent PM with one parasitic motion, 2PRU-PUU PM, are analyzed, demonstrating the effectiveness of the proposed type synthesis method.

Comprehensive Performance Optimization of a New Reconfigurable Two-Wheeled Self-Balancing Robot Based on Virtual Equivalent Parallel Mechanism

Comprehensive Performance Optimization of a New Reconfigurable Two-Wheeled Self-Balancing Robot Based on Virtual Equivalent Parallel Mechanism

An Approach for Modeling and Performance Analysis of Three-Leg Landing Gear Mechanisms Based on the Virtual Equivalent Parallel Mechanism

In order to realize the safe taking-off and landing of aircrafts on unstructured terrains, the landing gear on the aircraft is required to have a terrain-adaptive function. As a kind of aircraft onboard equipment, adaptive landing gear puts forward higher requirements for its design. This article proposes a virtual equivalent parallel mechanism (VEPM) modeling and performance analysis approach for the landing gear mechanism with three kinematic branch chains. In this approach, the unstructured terrain data were mapped to a moving platform. The moving platform, virtual restrained chains and the original mechanism of the landing gear mechanism combines the VEPM. In this way, the performance analysis object of the landing gear can be converted from a single kinematic branch to the entire system. The new approach can more effectively evaluate the overall motion performance and stability performance of the landing gear, and can help improve the structural design and control algorithm design of the spacecraft landing gear.

Mobility and singularity analyses of a symmetric multi-loop mechanism for space applications

A symmetric, double-tripod multi-loop mechanism (DTMLM), for aerospace applications, is the subject of this paper. Its mobility and singularity are analyzed, while introducing a novel tool, the cell-division method for singularity analysis, applicable to multi-loop mechanisms. The key principle of this method lies in replacing the singularity analysis of the original multi-loop mechanism with: (1) that of an equivalent simpler parallel mechanism; (2) the constraint analysis between loops; and (3) the singularity analysis of simpler kinematic subchains. Then, the mechanism is transformed into a simpler, equivalent parallel mechanism with three identical kinematic subchains. Its mobility and singularity are analyzed based on screw algebra, which leads to a key conclusion about the geometric properties of this mechanism. Results show that: (a) the DTMLM has three degrees of freedom (dof), i.e., two rotational dof around two intersecting axes lying in the middle plane of the mechanism, and one translational dof along the normal to the said plane (2R1T); and (b) the singularities of the 3-RSR parallel mechanism are avoided in the DTMLM by means of prismatic joints, singularities in the DTMLM occurring on the boundary of its workspace. Thus, the DTMLM has a 2R1T mobility everywhere within its workspace. When a set of multi-loop mechanisms of this kind are stacked as modules to assemble a multi-stage manipulator for space applications, the modules can be designed so that, under paradigm operations, all individual loops operate within their workspace, safe from singularities.

A new concept of contact joint to model the geometric foot-environment contacts for efficiently determining possible stances for legged robots

The determination of stances is of vital importance for legged robots that work in challenging environments where the terrain may be composed of uneven and slippery surfaces. However, the exploitation of uneven and slippery footholds has not received much research interest in the robotic community. This article proposes an efficient method to determine possible stances that may consist of uneven and slippery footholds by analyzing the degrees of freedom (DOFs) of the body of a legged robot and the capability of the legged robot to control these DOFs. The concept of the contact joint is proposed to describe the allowable foot motion considering the geometric foot-environment contacts. By adding a contact joint to each support foot, an equivalent parallel mechanism is formed by a legged robot and the ground. Subsequently, constraint-screw systems associated with the aforementioned equivalent parallel mechanism can be obtained. Based on that, the DOFs of the body of the legged robot and the capability of the legged robot to control these DOFs can be analyzed, and the possible stances can be determined. Case studies demonstrated the proposed approach.

A novel parallel sensor with six rigid compliant limbs for measuring six- component force/torque

A novel parallel sensor with six rigid/compliant hybrid limbs and six standard force sensors is developed for measuring the six-component force/torque. The measuring theory and performances are studied. A prototype of the robot hybrid hands with the parallel sensor is developed. A prototype of the parallel sensor is built up and its merits and performances are analyzed. A statics equation among the forces of the standard force sensors and the whole external load and a stiffness model of the parallel sensor are established based on its equivalent parallel mechanism. The force/torque of the parallel sensor is measured under the given external load. The theoretical solutions of the statics model of the parallel sensor are obtained and verified by both the experimental measuring solutions of the prototype of the parallel sensor and the simulation solutions of a FE model.

Gait analysis of a radial symmetrical hexapod robot based on parallel mechanisms

Most gait studies of multi-legged robots in past neglected the dexterity of robot body and the relationship between stride length and body height. This paper investigates the performance of a radial symmetrical hexapod robot based on the dexterity of parallel mechanism. Assuming the constraints between the supporting feet and the ground with hinges, the supporting legs and the hexapod body are taken as a parallel mechanism, and each swing leg is regarded as a serial manipulator. The hexapod robot can be considered as a series of hybrid serial-parallel mechanisms while walking on the ground. Locomotion performance can be got by analyzing these equivalent mechanisms. The kinematics of the whole robotic system is established, and the influence of foothold position on the workspace of robot body is analyzed. A new method to calculate the stride length of multi-legged robots is proposed by analyzing the relationship between the workspaces of two adjacent equivalent parallel mechanisms in one gait cycle. Referring to service region and service sphere, weight service sphere and weight service region are put forward to evaluate the dexterity of robot body. The dexterity of single point in workspace and the dexterity distribution in vertical and horizontal projection plane are demonstrated. Simulation shows when the foothold offset goes up to 174 mm, the dexterity of robot body achieves its maximum value 0.1644 in mixed gait. The proposed methods based on parallel mechanisms can be used to calculate the stride length and the dexterity of multi-legged robot, and provide new approach to determine the stride length, body height, footholds in gait planning of multi-legged robot.

Basal Ganglia Circuits for Reward Value–Guided Behavior

The basal ganglia are equipped with inhibitory and disinhibitory mechanisms that enable a subject to choose valuable objects and actions. Notably, a value can be determined flexibly by recent experience or stably by prolonged experience. Recent studies have revealed that the head and tail of the caudate nucleus selectively and differentially process flexible and stable values of visual objects. These signals are sent to the superior colliculus through different parts of the substantia nigra so that the animal looks preferentially at high-valued objects, but in different manners. Thus, relying on short-term value memories, the caudate head circuit allows the subject's gaze to move expectantly to recently valued objects. Relying on long-term value memories, the caudate tail circuit allows the subject's gaze to move automatically to previously valued objects. The basal ganglia also contain an equivalent parallel mechanism for action values. Such flexible-stable parallel mechanisms for object and action values create a highly adaptable system for decision making.

Equivalent Method of Output Mobility Calculation for a Novel Multi-loop Coupled Mechanism

In view of the different structures between novel multi-loop coupled mechanisms and common parallel mechanisms, a novel method is proposed for output constraint and mobility analysis of multi-loop coupled mechanisms. Converting a coupled mechanism into a common parallel mechanism is the main idea. A rule is given to split the connection between input and output into several independent elements. Relative motions of the coupled-nod link in every element are analyzed based on screw theory, and the element including coupled structure is ultimately equivalent to a serial chain. Thus the whole coupled mechanism is equivalent to a parallel mechanism. Limb twist systems and limb constraint systems of the equivalent parallel mechanism are analyzed, and the output mobility is calculated by re-solving the reciprocal screws of the constraint screws. The proposed method is applied to a typical coupled mechanism, and the computed result is in accordance with the prototype, which shows that the equivalent method can effectively simplify the complicated structure and get the correct mobility.

Typical gait analysis of a six-legged robot in the context of metamorphic mechanism theory

The equivalent mechanism of the system is often considered as one specific mechanism in most existing studies of multi-legged robots, however the equivalent mechanism is varying while the robot moves on the ground. Four typical tripod period gaits of a radial symmetrical six-legged robot are analyzed. Similar to the metamorphic mechanism, the locomotion of multi-legged robot is considered as a series of varying hybrid serial-parallel mechanisms by assuming the constraints of the feet on the ground with hinges. One gait cycle is divided into several periods, and in different walking period there is a specific equivalent mechanism corresponding to it, and the walking process of multi-legged robot is composed by these series of equivalent mechanisms. Walking performance can be got by analyzing these series of equivalent mechanisms. Kinematics model of the equivalent mechanism is established, workspaces of equivalent mechanisms are illustrated by simulation and a concept of static stability workspace is proposed to evaluate the static stability of these four gaits. A new method to calculate the stride length of multi-legged robots is presented by analyzing the relationship between the workspace of two adjacent equivalent parallel mechanisms in one gait cycle. The stride lengths of four gaits are given by simulations. Comparison of stride length and static stability among these four typical tripod gaits are given. It has been proved that mixed gait and insect-wave gait II have better static stability than mammal kick-off gait and insect-wave gait I. Insect-wave gait II displays its advantage on stride length while the height of robot body lower than 87 mm, mammal kick-off gait has superiority on stride length while the height of robot body higher than 115 mm, and insect-wave gait I shows its shortcoming in stride length. The proposed method based on metamorphic theory and combining the footholds and body height of robot provides a new method to comprehensive analyze the performance of multi-legged robot.

Analysis on Size Optimization of Equivalent Parallel Mechanism of Stationary Ring of Swashplate

The configuration of equivalent parallel mechanism of stationary ring of helicopter swashplate,1-RRS-3-SPS-1-PS mechanism,is analyzed,then the mechanism’s influence coefficient matrices are obtained by using virtual mechanism method,and their validity through simulation curves of input speed and acceleration derived from influence coefficient method and differential coefficient method is testified.Considering the dimension and mass,the dynamics performance of the 1-RRS-3-SPS-1-PS parallel mechanism is also analyzed with global performance indices of velocity and acceleration and inertia force,and the performance atlases about variation trend of the relationship between the dimension and dynamics performance are obtained.Simultaneously,the best mechanism’s sizes which make the mechanism’s dynamic performance to be best are obtained through analyzing the performance atlases.The correctness and feasibility of the global performance indices are validated through entity simulation by means of Matlab.

On the Modeling of Passive Motion of the Human Knee Joint by Means of Equivalent Planar and Spatial Parallel Mechanisms

Recent literature in biomechanics has demonstrated that motion of the human knee joint in virtually unloaded conditions is guided in a single and complex path by the passive structures of the joint alone. It has been deduced that the joint behaves as a single degree of freedom mechanism. Early models, dated on beginning of this century, showed this in the sagittal plane only. The three dimensional motion has been recently modelled by means of equivalent parallel mechanisms, based also on experimental observations on knee specimens of two separate frictionless contacts and three isometric ligament fibres. The model of the joint is a key tool for a deeper understanding of the knee motion and the design of reliable and efficient prostheses. It also provides useful information for the planning of surgical intervention on the basic structures of the knee. The progress of this modelling is reported in this paper. A medical and biomechanical rationale for these studies is provided, together with a number of relevant publications. The pioneering planar four-bar linkage has been initially advanced to a single degree of freedom equivalent spatial mechanism characterised by plane-to-sphere contacts. The closure equations for this mechanism have been progressively simplified. Extensions to more complex articular surfaces have been also performed. The results reported for all these models demonstrate that the original model assumptions were valid and that refinements in articular surface descriptions are justified to a certain extent.